Identical grey patches placed on the black and white bars of a square wave grating appear to differ markedly in lightness: White's Effect. The difference in apparent lightness is in a direction opposite to simultaneous contrast, such that the grey patches on the white bars are more extensively bounded by black borders than by white ones yet appear darker than the grey patches on the black bars. The apparent lightness can be described phenomenologically either as exhibiting contrast with the bars upon which the patches are lying or as assimilation with the neighbouring bars. Here, we disambiguate the effects of contrast and assimilation in White's Effect by using bars that differ along orthogonal colour and luminance axes in DKL colour space. To measure the effect of stimulus background on a given patch, subjects adjust the appearance of a comparison patch presented on a variegated background such that it matches as closely as possibly the appearance of the target patch. At low spatial frequencies, we find that White's Effect is due predominantly to contrast with the bar upon which the patch is lying. At high spatial frequencies, the effect is strengthened by assimilation of a similar magnitude with the neighbouring bars. For individual observers, the magnitude of contrast and assimilation measured using colour-luminance stimuli provide a quantitative prediction of the strength of the traditional achromatic White's Effect.